Study on $\mathrm{{\rm Y}}(nS)$ $\to$ $B_{c}M$ decays

With anticipation of abundant Upsilons data sample at high-luminosity heavy-flavor experiments in the future, we studied nonleptonic two-body weak decays of $\mathrm{{\rm Y}}(nS)$ below the open-bottom threshold with $n$ $=$ $1$, $2$ and $3$. It is found that branching ratios for $\mathrm{{\rm Y}}(1S,2S,3S)$ $\to$ $B_c\rho$ decays are relatively large among upsilons decay into $B_{c}M$ final states ($M$ $=$ $\pi$ $\rho$, $K$ and $K^{\ast }$) and can reach up to ${10}^{-10}$, which is promisingly detected by experiments at the running LHC and forthcoming SuperKEKB.